Question

Use the magnitudes, rounded to two decimal places, of the 100 earthquakes included in the accompanying data set to construct a frequency distribution. Use a class width of 1.00 and begin with a lower class limit of 0.00. Does the frequency distribution appear to be a normal distribution? Click the icon to view the earthquake magnitudes. * Earthquake Magnitudes Construct the frequency distribution. Frequency Magnitude 0.00- (Type integers or decimals. Do not round.) 1.38 4.42 3.28 2.04 3.26 2.54 1.82 2.02 2.96 2.84 2.54 2.04 3.22 4.44 1.38 2.84 1.98 1.86 2.98 3.30 Magnitudes 1.46 1.28 0.78 3.98 1.28 2.42 2.66 5.92 1.78 2.52 0.00 1.30 3.68 1.98 3.10 1.64 2.68 1.06 1.98 1.58 1.58 4.50 4.90 3.58 1.68 2.82 2.02 2.72 1.86 0.70 1.64 2.66 1.10 2.52 0.16 1.28 3.64 1.98 3.14 3.96 1.30 2.44 1.48 1.28 0.78 2.70 1.88 0.90 4.50 4.94 3.58 2.02 1.58 1.56 1.70 2.84 2.02 2.62 5.96 1.82 1.42 0.38 3.54 2.92 0.82 2.52 2.90 2.50 2.48 2.78 2.48 2.90 0.62 0.52 1.38 2.76 2.52 2.88 2.50 3.56 Print Done

Answer 1

The frequency distribution of the Earthquake Magnitudes data is obtained by counting the number of times each category appeared.

The histogram for Earthquake Magnitudes data is obtained in excel by following these steps,

Step 1: Write the data values in excel.The screenshot is shown below,

A B C E 1 Earthquake Magnitudes 2 1.38 1.46 1.28 0.78 1.42 1.28 4.42 3.98 2.42 0.38 3.28 2.66 5.92 1.78 3.54 2.04 2.52 1.3 2.92 6 3.26 3.68 1.98 3.1 0.82 7 2.54 1.64 2.68 1.06 2.52 1.58 2.9 8 1.82 1.98 1.58 LL LC

Step 2: Make a column bin with values 1, 2, 3, 4, 5, 6.

Bin

1

2

3

4

5

6

Step 3: DATA > Data Analysis > Histogram > OK. The screenshot is shown below,

T PAGE LAYOUT FORMULAS DATA REVIEW VIEW neera Data Analysis ZA AZ Data Analysis Analysis Tools OK Correlation A Covariance Cancel Descriptive Statistics Exponential Smoothing F-Test Two-Sample for Variances Fourier Analysis Histogram Moving Average Random Number Generation Rank and Percentile Help H 2308029 X

Step 4: Insert Input Range: Earthquake Magnitudes column, Bin Range: bin column then OK. The screenshot is shown below,

A B D 1 Earthquake Magnitudes 1.42 2 1.38 1.46 1.28 0.78 3.98 2,42 3 4.42 1.28 0.38 Bin 1j 4 3.28 2.66 5.92 1.78 3.54 2.52 2i 2.04 0 1.3 2.92 6 3.26 3.68 1.98 3.1 0.82 31 4! 1.06 7 2.54 1.64 2.68 2.52 8 Histogram X Input 10 Input Range 11 OK SA$2:SES21 Cancel SG$4:SG$9 Bin Range: 12 Help Labels 13 14 Output options 15 Qutput Range SH$4 16 New Worksheet Ply: 17 O New Workbook 18 19 Pareto (sorted histogram) Cumulative Percentage Chart Output 20 21

The frequency is obtained. The screenshot is shown below,

A B D 1 Earthquake Magnitudes 1.42 2 1.38 1.46 1.28 0.78 3.98 2,42 3 4.42 1.28 0.38 Bin 1j 4 3.28 2.66 5.92 1.78 3.54 2.52 2i 2.04 0 1.3 2.92 6 3.26 3.68 1.98 3.1 0.82 31 4! 1.06 7 2.54 1.64 2.68 2.52 8 Histogram X Input 10 Input Range 11 OK SA$2:SES21 Cancel SG$4:SG$9 Bin Range: 12 Help Labels 13 14 Output options 15 Qutput Range SH$4 16 New Worksheet Ply: 17 O New Workbook 18 19 Pareto (sorted histogram) Cumulative Percentage Chart Output 20 21

Step 5: Select the Bin and frequency column then > INSERT > Recommended Chart > Clustured column. The screenshot is shown below,

Frequency 40 35 30 25 20 15 10 0 0.00-0.99 1.00-1.99 2.00-2.99 3.00-3.99 4.00-4.99 5.00-5.99 LC

From the histogram above we can see that, the earthquake magnitudes are normally distributed with slightly skewed to right.