Which expression is Pearson’s chi-square statistic? Here O i,E i are observed and expected frequencies,n is the number of observations, O and are the observed and expected means, and o, E are the corresponding standard deviations.

$\sqrt{\sum_{i=1}^n(O_i-\bar O)/(n-1)}$

$(\bar O-\mu)/(\sigma_o\sqrt n)$

GATE 2026 ES – Question 15

Mathematics Foundation · Probability and Statistics · 1 mark · Multiple choice

Which expression is Pearson’s chi-square statistic? Here $O_i,E_i$ are observed and expected frequencies,$n$ is the number of observations,$\bar O$ and $\mu$ are the observed and expected means, and $\sigma_o,\sigma_E$ are the corresponding standard deviations.

$\sum_{i=1}^n (O_i-E_i)^2/E_i$
$\sqrt{\sum_{i=1}^n(O_i-\bar O)/(n-1)}$
$(\bar O-\mu)/(\sigma_o\sqrt n)$
$\sigma_o^2/\sigma_E^2$

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Correct answer: (A) $\sum_{i=1}^n (O_i-E_i)^2/E_i$

Explanation

Pearson’s statistic adds the squared discrepancy in every category, normalized by that category’s expected frequency: $\chi^2=\sum_i(O_i-E_i)^2/E_i$. Squaring prevents cancellation and the expected-count denominator accounts for category scale. Thus **A**. The other printed expressions are not this goodness-of-fit statistic.

GATE 2026 ES – Question 15

Explanation

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