29:["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":1}] 2a:["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"Given that,"}}] 2b:["$","li","1",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":2}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"Mean of a, b, 8, 5, 10 = 6"}}]]}] 39:Tc1c,

\therefore\,\,\,

{{a + b + 8 + 5 + 10} \over 5} = 6

2c:["$","li","2",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":3}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"$39"}}]]}] 2d:["$","li","3",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":4}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"

\\Rightarrow \\,\\,\\,

a + b + 23 = 30"}}]]}] 2e:["$","li","4",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":5}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"

\\Rightarrow \\,\\,\\,

a + b = 7 ....... (1)"}}]]}] 3a:Tda7,Variance

= {{\sum {{{\left( {{x_i} - A} \right)}^2}} } \over n} = 6.8

2f:["$","li","5",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":6}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"$3a"}}]]}] 3b:T1cbf,

\Rightarrow \,\,\,{{{{\left( {6 - a} \right)}^2} + {{\left( {6 - b} \right)}^2} + {{\left( {6 - 8} \right)}^2} + {{\left( {6 - 5} \right)}^2} + {{\left( {6 - 10} \right)}^2}} \over 5} = 6.5

30:["$","li","6",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":7}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"$3b"}}]]}] 3c:T1054,

\Rightarrow \,\,\,{\left( {6 - a} \right)^2} + {\left( {6 - b} \right)^2} + 4 + 1 + 16 = 34

31:["$","li","7",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":8}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"$3c"}}]]}] 3d:Tbd8,

\Rightarrow {\left( {6 - a} \right)^2} + {\left( {6 - b} \right)^2} = 13

32:["$","li","8",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":9}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"$3d"}}]]}] 3e:T91a,

\Rightarrow \,\,\,{a^2} + {b^2} = 25

33:["$","li","9",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":10}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"$3e"}}]]}] 34:["$","li","10",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":11}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"By using (1) we get,"}}]]}] 3f:T98c,

{a^2} + \left( {7 - a} \right){}^2 = 25

35:["$","li","11",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":12}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"$3f"}}]]}] 36:["$","footer",null,{"className":"flex flex-wrap gap-2 border-t border-rule pt-4 text-[13px] text-ink-400","children":["JEE Main 2008 · Annual, Paper 1 · Q5424",["$","span",null,{"className":"text-rule-strong","children":"·"}],"Statistics"]}] 37:["$","section",null,{"className":"flex flex-col gap-3 border-t border-rule pt-6","children":[["$","h2",null,{"className":"m-0 text-[12px] font-semibold uppercase tracking-[0.06em] text-ink-400","children":["More on ","Statistics"]}],["$","ul",null,{"className":"m-0 flex list-none flex-col gap-2 p-0","children":[["$","li","2fb2fd3c-04f4-4184-9dbe-0e92fa8e4ac1",{"children":["$","$L8",null,{"href":"/q/the-mean-of-set-of-30-observations-is-75-if-eac-neBwTeBhdFgcTfYjwLPWU","className":"flex flex-col gap-0.5 rounded-xl bg-surface-card px-4 py-3 no-underline shadow-soft transition-shadow hover:shadow-lift","children":[["$","span",null,{"className":"text-[15px] font-bold text-ink-900","children":"Statistics"}],["$","span",null,{"className":"text-[13px] text-ink-400","children":"JEE Main 2018 · 15 Apr, Morning shift · Q5415"}]]}]}],["$","li","831b4773-fed4-49e2-8cce-765c8c611558",{"children":["$","$L8",null,{"href":"/q/in-a-class-of-100-students-there-are-70-boys-who-Y7H3QCu3IBSaOqbi","className":"flex flex-col gap-0.5 rounded-xl bg-surface-card px-4 py-3 no-underline shadow-soft transition-shadow hover:shadow-lift","children":[["$","span",null,{"className":"text-[15px] font-bold text-ink-900","children":"Statistics"}],["$","span",null,{"className":"text-[13px] text-ink-400","children":"JEE Main 2002 · Annual, Paper 1 · Q5409"}]]}]}],["$","li","57c98db4-f26e-4619-b0a8-b88783647ac4",{"children":["$","$L8",null,{"href":"/q/the-median-of-a-set-of-9-distinct-observations-i-S2CpfA5xzaUED7bD","className":"flex flex-col gap-0.5 rounded-xl bg-surface-card px-4 py-3 no-underline shadow-soft transition-shadow hover:shadow-lift","children":[["$","span",null,{"className":"text-[15px] font-bold text-ink-900","children":"Statistics"}],["$","span",null,{"className":"text-[13px] text-ink-400","children":"JEE Main 2003 · Annual, Paper 1 · Q5410"}]]}]}],["$","li","f17de467-58d1-4861-9a6a-022197703032",{"children":["$","$L8",null,{"href":"/q/if-in-a-frequency-distribution-the-mean-and-med-IEaBRIby7TZbChYp","className":"flex flex-col gap-0.5 rounded-xl bg-surface-card px-4 py-3 no-underline shadow-soft transition-shadow hover:shadow-lift","children":[["$","span",null,{"className":"text-[15px] font-bold text-ink-900","children":"Statistics"}],["$","span",null,{"className":"text-[13px] text-ink-400","children":"JEE Main 2005 · Annual, Paper 1 · Q5411"}]]}]}]]}]]}]

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