Math

QuestionCreate a frequency distribution for screw lengths: 3.720 to 3.770, class width 0.010. Follow these steps: 1. Find range. 2. Divide range by classes. 3. Determine class limits. 4. Tally lengths. 5. Count lengths in each class.

Studdy Solution

STEP 1

Assumptions1. The given screw lengths are in inches and are3.724,3.752,3.746,3.751,3.741,3.768,3.766,3.746,3.753,3.747,3.732,3.754,3.744,3.752,3.733,3.748,3.722,3.753,3.759,3.746,3.759,3.759,3.736,3.741. . The lower class limit is3.720 inches.
3. The class width is0.010 inches.

STEP 2

First, we need to find the range of the data. The range is the difference between the maximum and minimum values in the data set.
Range=MaximumvalueMinimumvalueRange = Maximum\, value - Minimum\, value

STEP 3

Now, plug in the given values for the maximum and minimum values to calculate the range.
Range=3.7683.722Range =3.768 -3.722

STEP 4

Calculate the range.
Range=3.7683.722=0.046Range =3.768 -3.722 =0.046

STEP 5

Next, we need to find the number of classes. This can be found by dividing the range by the class width.
Numberofclasses=Range/ClasswidthNumber\, of\, classes = Range / Class\, width

STEP 6

Now, plug in the given values for the range and class width to calculate the number of classes.
Numberofclasses=0.046/0.010Number\, of\, classes =0.046 /0.010

STEP 7

Calculate the number of classes.
Numberofclasses=0.046/0.010=4.6Number\, of\, classes =0.046 /0.010 =4.6Since the number of classes cannot be a decimal, we round it up to the nearest whole number. So, we have5 classes.

STEP 8

Now that we have the number of classes, we can determine the class limits. The lower class limit is given as3.720. The upper class limit for each class can be found by adding the class width to the lower limit of that class.
Upperclasslimit=Lowerclasslimit+ClasswidthUpper\, class\, limit = Lower\, class\, limit + Class\, width

STEP 9

Now, tally the screw lengths into the classes. For each screw length, determine which class it falls into and mark a tally in that class.

STEP 10

Finally, count the number of screw lengths in each class. This gives us the frequency distribution for the screw lengths.

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