Question

The results of the top ten distances (in meters) for men and women in a javelin competition are listed below.

$\begin{array}{c}\text{Men}:87.00,\text{92.80,85.52,89.95,86.46,83.64,91.31,81.80,80.56,82.82}\\ \text{Women}:63.11,61.01,65.78,58.45,69.53,61.60,62.08,64.69,61.94,60.91\end{array}$

1. Make frequency tables for both the men’s and women’s distances.
2. Use the frequency tables you made in part (a) to make histograms for the two sets of the data.
3. What conclusions can you make from the distributions of the data.

Short answer

The frequency tables are,

distance	Frequency for men
$80-82$	1
$82-84$	2
$84-86$	1
$86-88$	2
$88-90$	1
$90-92$	1
$92-94$	1

distance	Frequency for women
$58-60$	1
$60-62$	4
$62-64$	2
$64-66$	2
$66-68$	0
$68-70$	1

The histograms are as follows,

The distance thrown by the men’s is higher than the women.

Step-by-step solution

Part a. Step 1. Given Information.

The provided data values are,

$\begin{array}{c}\text{Men}:87.00,\text{92.80,85.52,89.95,86.46,83.64,91.31,81.80,80.56,82.82}\\ \text{Women}:63.11,61.01,65.78,58.45,69.53,61.60,62.08,64.69,61.94,60.91\end{array}$

Step 2. Frequency Table for Men.

Make intervals of equal size for the provided data. For each interval, count the number of tally marks and write the frequency.

distance	Frequency for men
$80-82$	1
$82-84$	2
$84-86$	1
$86-88$	2
$88-90$	1
$90-92$	1
$92-94$	1

Step 3. Frequency Table for Women.

Make intervals of equal size for the provided data. For each interval, count the number of tally marks and write the frequency.

distance	Frequency for women
$58-60$	1
$60-62$	4
$62-64$	2
$64-66$	2
$66-68$	0
$68-70$	1

Step 4. Conclusion.

The frequency tables are,

distance	Frequency for men
$80-82$	1
$82-84$	2
$84-86$	1
$86-88$	2
$88-90$	1
$90-92$	1
$92-94$	1

distance	Frequency for women
$58-60$	1
$60-62$	4
$62-64$	2
$64-66$	2
$66-68$	0
$68-70$	1

Part b.Step 1. Given Information.

The provided data values are,

$\begin{array}{c}\text{Men}:87.00,\text{92.80,85.52,89.95,86.46,83.64,91.31,81.80,80.56,82.82}\\ \text{Women}:63.11,61.01,65.78,58.45,69.53,61.60,62.08,64.69,61.94,60.91\end{array}$

Step 2. Histograms.

Draw the horizontal and vertical axes. Label the intervals on the horizontal axis and the frequencies on the vertical axis.

Construct a bar to show the frequency of each interval.

Step 3. Conclusion.

The histograms are as follows,

Part c.Step 1. Given Information.

The provided data values are,

Step 2. Explanation.

From the part (a) and (b) it can be observed that, the distance covered by the men’s is higher than the women.

Step 3. Conclusion.

The distance thrown by the men’s is higher than the women.