Question

for the given data, construct a frequency distribution and frequency histogram of the data using five classes. describe the shape of the histogram as symmetric, uniform, skewed left, or skewed right. data set: california pick three lottery 3 6 7 6 0 6 1 7 8 4 1 5 7 5 9 1 5 3 9 9 2 2 3 0 8 8 4 0 2 4 a. skewed left b. skewed right c. symmetric d. uniform

Explanation:

Step1: Determine class width

First, find the minimum and maximum values in the data - set. The minimum value is 0 and the maximum value is 9. The range $R=9 - 0=9$. Since we want 5 classes, the class width $w=\frac{R}{5}=\frac{9}{5}=1.8\approx2$.

Step2: Define the classes

The classes are: 0 - 1, 2 - 3, 4 - 5, 6 - 7, 8 - 9.

Step3: Count frequencies

For the class 0 - 1: Count the number of 0s and 1s. There are 5 zeros and 3 ones, so the frequency $f_1 = 8$.
For the class 2 - 3: There are 4 twos and 3 threes, so the frequency $f_2=7$.
For the class 4 - 5: There are 2 fours and 3 fives, so the frequency $f_3 = 5$.
For the class 6 - 7: There are 4 sixes and 3 sevens, so the frequency $f_4=7$.
For the class 8 - 9: There are 3 eights and 4 nines, so the frequency $f_5 = 7$.

Step4: Analyze shape

The frequencies are 8, 7, 5, 7, 7. The distribution is symmetric as the frequencies on either side of the middle - class (4 - 5) are relatively equal.

Answer:

C. symmetric