- A researcher recorded the time, \(t\) minutes, spent using a mobile phone during a particular afternoon, for each child in a club.
The researcher coded the data using \(v = \frac { t - 5 } { 10 }\) and the results are summarised in the table below.
| Coded Time (v) | Frequency ( \(\boldsymbol { f }\) ) | Coded Time Midpoint (m) |
| \(0 \leqslant v < 5\) | 20 | 2.5 |
| \(5 \leqslant v < 10\) | 24 | \(a\) |
| \(10 \leqslant v < 15\) | 16 | 12.5 |
| \(15 \leqslant v < 20\) | 14 | 17.5 |
| \(20 \leqslant v < 30\) | 6 | \(b\) |
$$\text { (You may use } \sum f m = 825 \text { and } \sum f m ^ { 2 } = 12012.5 \text { ) }$$
- Write down the value of \(a\) and the value of \(b\).
- Calculate an estimate of the mean of \(v\).
- Calculate an estimate of the standard deviation of \(v\).
- Use linear interpolation to estimate the median of \(v\).
- Hence describe the skewness of the distribution. Give a reason for your answer.
- Calculate estimates of the mean and the standard deviation of the time spent using a mobile phone during the afternoon by the children in this club.
\(\_\_\_\_\) VAYV SIHI NI JIIIM ION OC
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