Question

The following data are the resting pulse rates for 21 randomly selected individuals who were participants at a 10K race.

49 55 48 50 55 70 59 59 55 49 58 55 55 57 69 55 45 62 60 68 59

(a) Construct a stem-and-leaf plot of the pulse rates.

(b) Construct a boxplot of the pulse rates. Label all points.

(c) Describe the shape of the distribution of the pulse rates.

(d) The boxplot provides information about the distribution of pulse rates for what population?

Answer 1

a -

Stem-leaf plot for given data -

Stem	leaves
4	5899
5	055555578999
6	0289
7	0

A stem-leaf plot is a chart we can use to display data by splitting up each value in a dataset into a stem and a leaf. The stem for each value is simply the first digit of the value while leaf is the second digit of the value,

We can check that above stem-leaf plot is correct or not as follows-

1) number of individuals leaves matches the number of observations. so, we have total 21 leaves which matches 21 observations in our original dataset.

2) The very first leaf should match the minimum value in your dataset. So, in our example, we see that the first leaf is "5" and is paired with a stem of "4" which matches the minimum number of "45" in our dataset.

3) The very last leaf should match the maximum value in your dataset. So, in our example, we see that the last leaf is "0" and is paired with a stem of "7" which matches the maximum number of "70" in our dataset.

Hence, our stem-leaf plot is correct.

b -

Boxplot pulse rates is as follows -

Boxpoplot also known as box and whisker plots are a type of chart often used in explanatory data analysis to visually show the distribution of numerical data and skewness through displaying the data quartiles.

c -

From above box plot, we can see that value of median is approximately in the middle of the box and whiskers are about the same on both sides of the box, so distribution is symmetric. Hence, shape of the distribution of the pulse rates is symmetric.

d -

The boxplot provides information about the distribution of pulse rates for population that population is symmetric distribution. Approximately average pulse rates of participants at 10K race is 56. Maximum and minimum pulse rates of participants are 45 and 70 respectively.