Question

1. apply math models use the data in the given table.

a. bella collected data on the stride lengths of students. she wants to show the data so that the mean and range of stride lengths can be found. choose and make an appropriate display of the data.
table: stride length (cm) with values 84, 66, 59, 65, 67, 80, 74, 67, 78, 79
b. bella wants to show the median and the iqr of the stride lengths. choose and make an appropriate data display.

1. apply math models miguel collected data on different shoe types owned. he wants to compare the different shoe types to each other and to the total number of shoes owned. choose and make an appropriate display of the data.

table: shoe type (sandals, sneakers, high heels, slip ons) and number owned (23, 56, 10, 21)

Explanation:

Part 6a

Step1: List the data

First, we list out all the stride length data: 84, 66, 59, 65, 67, 80, 74, 67, 78, 79.

Step2: Choose a display (Dot Plot)

A dot plot is appropriate as it shows individual data points, making it easy to find the mean (by summing and dividing) and range (max - min). We create a number line from 59 to 84. For each data point, we place a dot above its value. So:

• 59: 1 dot
• 65: 1 dot
• 66: 1 dot
• 67: 2 dots
• 74: 1 dot
• 78: 1 dot
• 79: 1 dot
• 80: 1 dot
• 84: 1 dot

Step1: Recognize the need for a box plot

A box plot (box - and - whisker plot) is suitable for showing the median (middle value) and IQR (inter - quartile range, \(Q_3 - Q_1\)).

Step2: Order the data

First, order the stride length data: 59, 65, 66, 67, 67, 74, 78, 79, 80, 84.

Step3: Find the median

Since there are 10 data points (even number), the median is the average of the 5th and 6th values. The 5th value is 67 and the 6th is 74. So median \(=\frac{67 + 74}{2}=70.5\).

Step4: Find \(Q_1\) and \(Q_3\)

The lower half of the data (first 5 values: 59, 65, 66, 67, 67) has a median ( \(Q_1\)) of 66. The upper half (last 5 values: 74, 78, 79, 80, 84) has a median ( \(Q_3\)) of 79.

Step5: Create the box plot

Draw a number line from 59 to 84. Draw a box from \(Q_1 = 66\) to \(Q_3=79\). Draw a line inside the box at the median (70.5). Draw whiskers from the minimum (59) to \(Q_1\) and from \(Q_3\) to the maximum (84).

Step1: Recognize the need for a circle graph (pie chart)

A pie chart is appropriate when we want to compare parts (different shoe types) to each other and to the whole (total number of shoes).

Step2: Calculate the total number of shoes

First, find the total number of shoes. Sandals: 23, Sneakers: 56, High heels: 10, Slip ons: 21. Total \(=23 + 56+10 + 21=110\).

Step3: Calculate the percentage for each shoe type

• Sandals: \(\frac{23}{110}\times100\%\approx20.91\%\)
• Sneakers: \(\frac{56}{110}\times100\%\approx50.91\%\)
• High heels: \(\frac{10}{110}\times100\%\approx9.09\%\)
• Slip ons: \(\frac{21}{110}\times100\%\approx19.09\%\)

Step4: Create the pie chart

Divide a circle into sectors with central angles proportional to the percentages. For example, the central angle for sandals is \(0.2091\times360\approx75.28^\circ\), for sneakers \(0.5091\times360\approx183.28^\circ\), for high heels \(0.0909\times360\approx32.72^\circ\), and for slip ons \(0.1909\times360\approx68.72^\circ\). Label each sector with the shoe type and its percentage.

Answer:

A dot plot is appropriate. The data points (stride lengths in cm) are plotted as: 59 (1 dot), 65 (1), 66 (1), 67 (2), 74 (1), 78 (1), 79 (1), 80 (1), 84 (1) on a number line from 59 to 84.

Part 6b