1) A botanist opened a sample of 50 bean pods and counted the number of beans in each pod. The results obtained were as follows:
1 2 0 1 2 5 4 0 2 1
6 5 4 4 1 6 0 4 0 1
6 4 5 5 0 6 6 2 3 6
2 5 0 3 1 3 1 5 3 3
1 1 2 1 3 1 4 2 6 3
a) Fill in the frequency table for these data.
Number of Beans in Pod = Number of Bean Pods
0 = ________
1 = ________
2 = ________
3 = ________
4 = ________
5 = ________
6 = ________
b) Determine the mode of the data.
Mode = _______
Round your answer to 2 decimal places as needed.
c) Determine the median of the data.
Median = ________
Round your answer to 2 decimal places as needed.
d) Calculate the mean ( ¯¯¯ X ) of the data.
Mean = ______
Round your answer to 2 decimal places as needed.
e) Calculate the standard deviation ( S ) using your graphing calculator. (5 points)
Hint: Also verify that the mean you calculated in part d matches the mean from the calculator.
Standard deviation = ________
Round your answer to 2 decimal places as needed.
f) Determine the range of variation:
(¯¯¯X−S,¯¯¯X+S) = ( _______, _______ )
Round your answers to 2 decimal places as needed.
g) Calculate what percent of the data values are within one standard deviation of the mean.
Hint: Create a histogram on paper and shade the included region(s) on your histogram to help visualize the shaded area and help with calculations.
Total area of shaded region = ______
Round your answer to 2 decimal places as needed.
Percent of area within one standard deviation = _____%
Round your answer to 2 decimal places as needed.
