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a) Find the measures of central tendency for the boys:
157, 178, 167, 152, 185, 176, 175, 183, 166, 160, 172, 178, 151, 172, 165, 166.

b) Find the measures of central tendency for the girls:
179, 173, 175, 167, 168, 173.

Answer :

To find the measures of central tendency for both the boys' and girls' heights, we will calculate the mean, median, and mode for each set of data.

a) Boys' Heights: 157, 178, 167, 152, 185, 176, 175, 183, 166, 160, 172, 178, 151, 172, 165, 166.

  1. Mean (Average):

    • Add all the heights together and then divide by the number of boys.

    [tex]\text{Mean} = \frac{157 + 178 + 167 + 152 + 185 + 176 + 175 + 183 + 166 + 160 + 172 + 178 + 151 + 172 + 165 + 166}{16}[/tex]

    [tex]\text{Mean} = \frac{2703}{16} = 168.9375[/tex]

    So, the mean height of the boys is approximately 168.94 cm.

  2. Median:

    • First, arrange the heights in ascending order: 151, 152, 157, 160, 165, 166, 166, 167, 172, 172, 175, 176, 178, 178, 183, 185.
    • Since there are 16 numbers, the median will be the average of the 8th and 9th values.

    [tex]\text{Median} = \frac{167 + 172}{2} = 169.5[/tex]

    So, the median height of the boys is 169.5 cm.

  3. Mode:

    • The mode is the most frequently occurring height.
    • Here, 166 and 178 both appear twice, making them the modes.

    So, the modes of the boys' heights are 166 cm and 178 cm.

b) Girls' Heights: 179, 173, 175, 167, 168, 173.

  1. Mean (Average):

    • Add all the heights together and then divide by the number of girls.

    [tex]\text{Mean} = \frac{179 + 173 + 175 + 167 + 168 + 173}{6}[/tex]

    [tex]\text{Mean} = \frac{1035}{6} = 172.5[/tex]

    So, the mean height of the girls is 172.5 cm.

  2. Median:

    • First, arrange the heights in ascending order: 167, 168, 173, 173, 175, 179.
    • Since there are 6 numbers, the median will be the average of the 3rd and 4th values.

    [tex]\text{Median} = \frac{173 + 173}{2} = 173[/tex]

    So, the median height of the girls is 173 cm.

  3. Mode:

    • The mode is the most frequently occurring height.
    • Here, 173 appears twice, making it the mode.

    So, the mode of the girls' heights is 173 cm.

In summary, the measures of central tendency help us understand the distribution of the data better by providing a central value that represents the entire dataset. Each measure gives us a slightly different perspective on the data.

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