2. the test scores from mrs. grays math class are shown below. 72, 73, 66, 71, 82, 85, 95, 85, 86, 89, 91…

2. the test scores from mrs. grays math class are shown below. 72, 73, 66, 71, 82, 85, 95, 85, 86, 89, 91, 92 construct a box - and - whisker plot to display these data. 3. in the box - and - whisker plot below, what is the 2nd quartile? 4. below are two representations of data. a: 2, 5, 5, 6, 6, 6, 7, 8, 9 which statement about a and b is true? 1) median of a > median of b 2) range of a < range of b 3) upper quartile of a < upper quartile of b 4) lower quartile of a > lower quartile of b

2. the test scores from mrs. grays math class are shown below. 72, 73, 66, 71, 82, 85, 95, 85, 86, 89, 91, 92 construct a box - and - whisker plot to display these data. 3. in the box - and - whisker plot below, what is the 2nd quartile? 4. below are two representations of data. a: 2, 5, 5, 6, 6, 6, 7, 8, 9 which statement about a and b is true? 1) median of a > median of b 2) range of a < range of b 3) upper quartile of a < upper quartile of b 4) lower quartile of a > lower quartile of b

Answer

Explanation:

Step1: Recall box - and - whisker plot concepts

The 2nd quartile (Q2) of a box - and - whisker plot is the median.

Step2: Identify the median on the box - and - whisker plot for question 3

The line inside the box represents the median (2nd quartile). Looking at the box - and - whisker plot in question 3, the value of the line inside the box is 25.

Step3: Calculate median, range, lower and upper quartiles for data set A in question 4

For data set A: 2, 5, 5, 6, 6, 6, 7, 8, 9. There are n = 9 data points. The median (Q2) of a data - set with n data points (n odd) is the $\left(\frac{n + 1}{2}\right)$-th value. So, $\frac{9+1}{2}=5$ - th value, which is 6. The lower half of the data is 2, 5, 5, 6. The lower quartile (Q1) is the median of the lower half. Since there are 4 data points in the lower half, Q1=$\frac{5 + 5}{2}=5$. The upper half of the data is 6, 7, 8, 9. The upper quartile (Q3) is the median of the upper half. Since there are 4 data points in the upper half, Q3=$\frac{7+8}{2}=7.5$. The range of A is 9 - 2=7.

Step4: Analyze box - and - whisker plot for data set B in question 4

From the box - and - whisker plot of B, the median is around 7, the lower quartile is around 4, and the upper quartile is around 9, and the range is approximately 11 - 3 = 8.

  1. Median of A = 6, median of B≈7, so median of A<median of B.
  2. Range of A = 7, range of B≈8, so range of A<range of B.
  3. Upper quartile of A = 7.5, upper quartile of B≈9, so upper quartile of A<upper quartile of B.
  4. Lower quartile of A = 5, lower quartile of B≈4, so lower quartile of A>lower quartile of B.

Step5: Construct box - and - whisker plot for question 2

First, order the data: 66, 71, 72, 73, 82, 85, 85, 86, 89, 91, 92. There are n = 11 data points. The median (Q2) is the $\left(\frac{11 + 1}{2}\right)$-th value, which is the 6 - th value, so Q2 = 85. The lower half of the data is 66, 71, 72, 73, 82. The lower quartile (Q1) is the $\left(\frac{5+1}{2}\right)$-th value of the lower half, which is 72. The upper half of the data is 85, 86, 89, 91, 92. The upper quartile (Q3) is the $\left(\frac{5 + 1}{2}\right)$-th value of the upper half, which is 89. The minimum value is 66 and the maximum value is 92. We draw a number line and mark the minimum (66), Q1 (72), Q2 (85), Q3 (89), and maximum (92). Then we draw a box from Q1 to Q3 with a line at Q2 and whiskers from the box to the minimum and maximum values.

Answer:

  1. Box - and - whisker plot constructed with minimum = 66, Q1 = 72, Q2 = 85, Q3 = 89, maximum = 92.
    1. 25
    1. upper quartile of A < upper quartile of B