The following data represent the record high temperatures for each of the 50 states:

112, 100, 127, 120, 134, 118, 105, 110, 109, 112, 110, 118, 117, 116, 118, 122, 114, 114, 105, 112, 107, 112, 114, 115, 118, 117, 118, 122, 106, 110, 116, 108, 110, 121, 113, 120, 119, 111, 104, 111, 120, 113, 120, 117, 105, 110, 118, 112, 114, 144.

a. Construct the stem-and-leaf plot.

b. Construct a frequency distribution table with 4 classes.

c. Calculate the mean, median, and mode.

d. Calculate the variance and standard deviation.

e. Calculate the interquartile range.

a. The stem and leaf plot for the given data can be constructed to visually represent the distribution of the record high temperatures for each state.

b. A frequency distribution table with 4 classes can be created to organize the data into intervals and count the number of occurrences within each interval.

c. The mean, median, and mode can be calculated to provide measures of central tendency for the data set.

d. The variance and standard deviation can be computed to determine the spread or variability of the data.

e. The interquartile range can be calculated to measure the dispersion of the middle 50% of the data.

a. To construct the stem and leaf plot, we separate each temperature value into a stem and leaf. The stem represents the tens digit, while the leaf represents the units digit. Here is the stem and leaf plot for the given data:

10 | 4

11 | 045566677899

12 | 011224

13 | 0013334445555778

14 | 4

b. To create a frequency distribution table with 4 classes, we divide the range of the data into four equal intervals. The classes and their corresponding frequencies are as follows:

104-113: 15

114-123: 19

124-133: 7

134-143: 2

c. The mean is calculated by summing all the values and dividing by the total number of values. The median is the middle value when the data is arranged in ascending order. The mode is the value that appears most frequently in the data set. In this case:

Mean: 115.68

Median: 116

Mode: 118

d. The variance measures the average squared deviation from the mean, while the standard deviation is the square root of the variance. Using the appropriate formulas, the variance is approximately 53.75, and the standard deviation is approximately 7.33.

e. The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). By ordering the data and calculating the quartiles, we find:

Q1: 110

Q3: 118

IQR: 8

These calculations provide a summary of the distribution and characteristics of the given data set of record high temperatures for each state.

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