Question

here is a data set:
4.97 5.04 4.64 3.53
5.18 5.38 5.21 3.97
3.97 5.09 4.96 4.61
5.95 4.75 4.18 4.31
4.91 4.96 4.53 5.63
5.28 4.66 4.46 4.85
4.31 5.46 3.75 4.88

construct a grouped frequency distribution table (gfdt) for this data set. you want 10 classes with a
ice\ class width. your classes should be labeled using interval notation. each class contains its lower class limit, and the lower class limits should all be multiples of the class width. in that the data appears to be discrete, use a closed-interval to label each class.

data range | frequency
--- | ---

Explanation:

Step1: Find min, max of data

Min = 3.53, Max = 5.95

Step2: Calculate class width

Range = $5.95 - 3.53 = 2.42$
Class width = $\frac{2.42}{10} \approx 0.25$ (nice width, multiple of 0.25)

Step3: Set lower class limits

Start at 3.50 (multiple of 0.25, ≤ min):
$3.50, 3.75, 4.00, 4.25, 4.50, 4.75, 5.00, 5.25, 5.50, 5.75$

Step4: Define closed intervals

Each interval: $[L, L+0.24]$ (since discrete, avoid overlap)

Step5: Count frequencies per interval

Tally data points in each class:

• $[3.50, 3.74]$: 3.53, 3.75? No, 3.75 is next lower limit. Correct: 3.53 → 1
• $[3.75, 3.99]$: 3.97, 3.97, 3.75 → 3
• $[4.00, 4.24]$: 4.18 → 1
• $[4.25, 4.49]$: 4.31, 4.31, 4.46 → 3
• $[4.50, 4.74]$: 4.64, 4.61, 4.53, 4.66 → 4
• $[4.75, 4.99]$: 4.97, 4.75, 4.91, 4.96, 4.96, 4.85, 4.88 → 7
• $[5.00, 5.24]$: 5.04, 5.18, 5.21, 5.09 → 4
• $[5.25, 5.49]$: 5.38, 5.28, 5.46 → 3
• $[5.50, 5.74]$: 5.63 → 1
• $[5.75, 5.99]$: 5.95 → 1

Answer:

Data range	Frequency
$[3.75, 3.99]$	3
$[4.00, 4.24]$	1
$[4.25, 4.49]$	3
$[4.50, 4.74]$	4
$[4.75, 4.99]$	7
$[5.00, 5.24]$	4
$[5.25, 5.49]$	3
$[5.50, 5.74]$	1
$[5.75, 5.99]$	1