1. The table below shows the distances (to the nearest km ) travelled to work by the 50 employees in an office.

$$\text { [You may use } \left. \sum \mathrm { f } x = 394 , \quad \sum \mathrm { f } x ^ { 2 } = 6500 \right]$$ A histogram has been drawn to represent these data.
The bar representing the distance of \(3 - 5\) has a width of 1.5 cm and a height of 6 cm .

1. Calculate the width and height of the bar representing the distance of 6-10
2. Use linear interpolation to estimate the median distance travelled to work.
3. 1. Show that an estimate of the mean distance travelled to work is 7.88 km .
   2. Estimate the standard deviation of the distances travelled to work.
4. Describe, giving a reason, the skewness of these data. Peng starts to work in this office as the \(51 ^ { \text {st } }\) employee.
   She travels a distance of 7.88 km to work.
5. Without carrying out any further calculations, state, giving a reason, what effect Peng's addition to the workforce would have on your estimates of the
   1. mean,
   2. median,
   3. standard deviation
      of the distances travelled to work.