1
39 63 wind speed (km h )
–1
Measurements of wind speed on a certain island were taken over a period of one year. A box-andwhisker
plot of the data obtained is displayed above, and the values of the quartiles are as shown.
It is suggested that wind speed can be modelled approximately by a normal distribution with mean
µ km h−1
and standard deviation σ km h−1
.
(i) Estimate the value of µ. [1]
(ii) Estimate the value of σ. [
u = (63+39)/2=51
To estimate the value of µ (mean) and σ (standard deviation) for wind speed, we can use the information given in the box-and-whisker plot.
In a box-and-whisker plot, the box represents the interquartile range (IQR), which is the range between the first quartile (Q1) and the third quartile (Q3). The whiskers represent the minimum and maximum values within 1.5 times the IQR from the box.
From the plot, we can see that the lower whisker extends down to -1, which implies that there are measurements below -1 km/h. However, since wind speeds cannot be negative, this indicates a data error. Therefore, we can ignore this value and assume that the minimum value is at the lower end of the box.
(i) To estimate the value of µ (mean), we can use the median, which is represented by the line inside the box in the plot. From the plot, we can estimate that the median is around 39 km/h.
(ii) To estimate the value of σ (standard deviation), we can use the range between the first quartile (Q1) and the third quartile (Q3), which is the interquartile range (IQR) represented by the height of the box in the plot. From the plot, we can estimate that the IQR is around 63-39 = 24 km/h.
However, note that this estimation assumes that the data is normally distributed, which may or may not be the case. To obtain more accurate estimates for µ and σ, it would be ideal to have a larger sample size or access to a complete dataset.