the stem - and - leaf plot below shows the number of pages each student in a class read the previous…

Explanation:

Step1: Write out the data - set

The data - set from the stem - and - leaf plot is: 0, 0, 5, 8, 12, 13, 15, 18, 18, 19, 22, 24, 26, 27, 27, 27, 33, 35, 36, 42, 44, 46, 57. There are (n = 23) data points.

Step2: Calculate the median

Since (n = 23) (an odd number), the median is the (\left(\frac{n + 1}{2}\right))-th value. (\frac{23+1}{2}=12) - th value. Arranging the data in ascending order, the 12 - th value is 24.

Step3: Calculate the mode

The mode is the most frequently occurring value. The value 27 occurs 3 times, so the mode is 27. Since (24<27), the median is less than the mode.

Step4: Calculate the range

The range is the difference between the maximum and minimum values. The maximum value is 57 and the minimum value is 0. Range (=57 - 0=57\neq52).

Step5: Calculate the first quartile

The first quartile (Q_1) is the median of the lower half of the data. The lower half of the 23 - data - point set consists of the first 11 values. Since (n_1 = 11) (an odd number), the median of the lower half is the (\left(\frac{11 + 1}{2}\right)=6) - th value. The 6 - th value of the lower half of the data (0, 0, 5, 8, 12, 13, 15, 18, 18, 19, 22) is 13.

Step6: Check for symmetry

The data is not symmetric as the distribution of values is not evenly balanced around the center.

Answer:

The value of the first quartile is 13.