Saturday, August 21, 2021

A study has shown that males in the UK have steadily grown in height from the 1800s to 1980. Based on the data below, find the mean height for each sixty-year period. Then, choose an appropriate chart or plot to visualize this data. Year Height in Cm 1810 169.7 1820 169.1 1830 166.7 1840 166.5 1850 165.6 1860 166.6 1870 167.2 1880 168 1890 167.4 1900 169.4 1910 170.9 1920 171 1930 173.9 1940 174.9 1950 176 1960 176.9 1970 177.1 1980 176.8

Problem 

A study has shown that males in the UK have steadily grown in height from the 1800s to 1980. Based on the data below, find the mean height for each sixty-year period. Then, choose an appropriate chart or plot to visualize this data.

YearHeight in Cm
1810169.7
1820169.1
1830166.7
1840166.5
1850165.6
1860166.6
1870167.2
1880168
1890167.4
1900169.4
1910170.9
1920171
1930173.9
1940174.9
1950176
1960176.9
1970177.1
1980176.8

 

Solution 

Here, we need to:

  • Find the mean of each period
  • Plot this data

First, we find the mean by applying the formula for the mean,

  \[ \bar{x} = \frac{\Sigma x_{i}}{n} \]

YearHeight in Cm
1810 - 1860

  \[ \dfrac{169.7+169.1+166.7+166.5+165.6+166.6}{6} = \]

  \[ \dfrac{1004.2}{6} \]

  \[ = 167.4 \]

1870 - 1920

  \[ \dfrac{167.2+168+167.4+169.4+170.9+171}{6} = \]

  \[ \dfrac{1013.9}{6} \]

  \[ = 169 \]

1930 - 1980

  \[ \dfrac{173.9+174.9+176+176.9+177.1+176.8}{6} = \]

  \[ \dfrac{1055.6}{6} \]

  \[ = 175.9 \]

 

As we can see, the average height increases over time. This becomes even more apparent when we plot the data.

Bar chart 2

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