The following grouped data represent the marks obtained by students in a mathematics test.

$$\begin{array}{c|c}
\text{Score interval (marks)} & \text{Frequency} \ \hline
0\!\text{-}\!9 & 2\
10\!\text{-}\!19 & 5\
20\!\text{-}\!29 & a\
30\!\text{-}\!39 & 7\
40\!\text{-}\!49 & 4\
50\!\text{-}\!59 & b
\end{array}$$

The total number of students is 30 and the mean mark is $27.5$.
(i) Determine the missing frequencies $a$ and $b$.
(ii) Using the class mid‑points as representative values, calculate the estimated standard deviation of the marks (to one decimal place).

Question

The following grouped data represent the marks obtained by students in a mathematics test.

$$\begin{array}{c|c}
\text{Score interval (marks)} & \text{Frequency} \ \hline
0\!\text{-}\!9 & 2\
10\!\text{-}\!19 & 5\
20\!\text{-}\!29 & a\
30\!\text{-}\!39 & 7\
40\!\text{-}\!49 & 4\
50\!\text{-}\!59 & b
\end{array}$$

The total number of students is 30 and the mean mark is $27.5$.  
(i) Determine the missing frequencies $a$ and $b$.  
(ii) Using the class mid‑points as representative values, calculate the estimated standard deviation of the marks (to one decimal place).

Accepted Answer

a = 11, b = 1, estimated standard deviation ≈ 11.9

Neco Model Questions Vol1 2025 Mathematics Question 48

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