33:T850,Mean =

{{3 + 5 + 7 + a + b} \over 5}

= 528:["$","li","0",{"className":"flex items-start gap-3","children":[["$","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":1}],["$","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":"$33"}}]]}] 29:["$","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":"

\\Rightarrow

a

+ b = 10"}}]]}] 34:T107c,Variance =

{{{3^2} + {5^2} + {7^2} + {a^2} + {b^2}} \over 5}

- (5)² = 42a:["$","li","2",{"className":"flex items-start gap-3","children":[["$","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":"$34"}}]]}] 35:T7cd,

\Rightarrow

{{a^2} + {b^2}}

= 622b:["$","li","3",{"className":"flex items-start gap-3","children":[["$","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":"$35"}}]]}] 36:T871,

\Rightarrow

{\left( {a + b} \right)^2} - 2ab

= 622c:["$","li","4",{"className":"flex items-start gap-3","children":[["$","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":"$36"}}]]}] 2d:["$","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":"

\\Rightarrow

ab

= 19"}}]]}] 2e:["$","li","6",{"className":"flex items-start gap-3","children":[["$","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":"So

a

and b are the roots of the equation"}}]]}] 2f:["$","li","7",{"className":"flex items-start gap-3","children":[["$","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}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"x² – 10x + 19 = 0"}}]]}] 30:["$","footer",null,{"className":"flex flex-wrap gap-2 border-t border-rule pt-4 text-[13px] text-ink-400","children":["JEE Main 2020 · 5 Sep, Evening shift · Q5453",["$","span",null,{"className":"text-rule-strong","children":"·"}],"Statistics"]}] 31:["$","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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