The problem presents a set of data representing the number of steps Cora walks each day: 7,773, 8,454, 5,500, 9,000, 7,316, 8,546, 8,227, 6,684. The task is to determine which of the two given box plots correctly represents this data.

1. Problem Description

The problem presents a set of data representing the number of steps Cora walks each day: 7,773, 8,454, 5,500, 9,000, 7,316, 8,546, 8,227, 6,

6

8

4. The task is to determine which of the two given box plots correctly represents this data.

2. Solution Steps

First, we need to find the key values for creating a box plot: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.

Step 1: Order the data from least to greatest:

5,500, 6,684, 7,316, 7,773, 8,227, 8,454, 8,546, 9,000

Step 2: Identify the minimum and maximum values:

Minimum = 5,500

Maximum = 9,000

Step 3: Calculate the median (Q2). Since there are 8 data points (an even number), the median is the average of the middle two values.

Median = $(7773 + 8227)/2 = 16000/2 = 8,000$

Step 4: Calculate the first quartile (Q1). Q1 is the median of the lower half of the data (excluding the median if the number of data points is odd, which in this case it isn't).

Lower half: 5,500, 6,684, 7,316, 7,773

Q1 = $(6684+7316)/2 = 14000/2 = 7,000$

Step 5: Calculate the third quartile (Q3). Q3 is the median of the upper half of the data.

Upper half: 8,227, 8,454, 8,546, 9,000

Q3 = $(8454+8546)/2 = 17000/2 = 8,500$

Step 6: Examine the box plots and compare them to the calculated values.

The first box plot has:

Minimum around 5,500

Q1 around 7,000

Median around 8,000

Q3 around 8,500

Maximum around 9,000

The second box plot has:

Minimum around 5,500

Q1 close to 7,

2

5

0. Median around 7,750

Q3 around 8,250

Maximum around 9,000

The first box plot matches our calculated values more closely.

3. Final Answer

The first box plot represents the data.