Question In a class of 30 students there are 15 girls and 15 boys. Their heights

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Question
In a class of 30 students there are 15 girls and 15 boys. Their heights are measured (in metres) and are lised below.
Boys: 1.65; 1.71; 1.59; 1.74; 1.66; 1.69; 1.72; 1.66; 1.65; 1.64; 1.68; 1.74; 1.57; 1.59; 1.80;
Girls: 1.66; 1.69; 1.58; 1.55; 1.51; 1.56; 1.64; 1.69; 1.70; 1.57; 1.52; 1.58; 1.64; 1.68; 1.67;
(i) display this information in a back-to-back stem-and-leaf plot.
(ii) calculate the median heights for boys and girls.
(iii) write a PEEL paragraph comparing the heights of the boys and girls with specific. Reference to median and range.

Explanation / Answer

(i) To draw the stem and leaf diagram we first write the given data in ascending order. So for boys first the heights are:

1.57, 1.59, 1.59, 1.64, 1.65, 1.65 1.66, 1.66, 1.68, 1.69, 1.71, 1.72, 1.74, 1.74, 1.8

This is converted into a stem and leaf diagram as:

STEM    LEAF

1.5         7 9 9

1.6         4 5 5 6 6 8 9

1.7         1 2 4 4

1.8         0

Similarly now for girls, the data would be displayed as:

Ascending order: 1.51, 1.52, 1.55, 1.56, 1.57, 1.58, 1.58, 1.64, 1.64, 1.66, 1.67, 1.68, 1.69, 1.69, 1.70

This is converted into a stem and leaf diagram as:

STEM    LEAF

1.5         1 2 5 6 7 8 8

1.6         4 4 6 7 8 9 9

1.7         0

(ii) For both boys and girls, as we have data for 15 for each of them the middle value of the data that is the 8th value would be the median. This is computed as:

Medianboys = 1.66

Mediangirls = 1.64

(iii) Here we can clearly see from the stem and leaf diagram that the mean height of the boys seems to be greater than the mean height of the girls as there are less values at the top part of the stem and leaf diagram in case of boys and not so with girls.

Also using median height also we could see that the median height of boys is greater than that of girls

Rangeboys= 1.80 - 1.57 = 0.23

Rangegirls = 1.70 - 1.51 = 0.19

This shows that the spread of heights in boys is comparatively greater than the spread of heights in girls.

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