Question

a. data: 42, 58, 67, 55, 40, 69, 66, 51, 46, 48, 68
1 what is the lower extreme
2 what is the upper extreme
3 what is the median
4 what is the lower quartile
5 what is the upper quartile
6 what is the range
7 what is the interquartile range
8 what is the mean
9 what is the model

b. data: 14, 11, 8, 1, 23, 20, 17, 5, 19, 10, 12, 22
1 what is the lower extreme
2 what is the upper extreme
3 what is the median
4 what is the lower quartile
5 what is the upper quartile
6 what is the range
7 what is the interquartile range
8 what is the mean
9 what is the model

Explanation:

Step1: Sort Dataset A

$40, 42, 46, 48, 51, 55, 58, 66, 67, 68, 69$

Step2: Find Dataset A extremes

Lower extreme = smallest value: $40$
Upper extreme = largest value: $69$

Step3: Calculate Dataset A median

Middle value of 11 terms (6th term): $55$

Step4: Find Dataset A quartiles

Lower quartile (Q1): median of first 5 terms: $46$
Upper quartile (Q3): median of last 5 terms: $67$

Step5: Compute Dataset A range

Range = upper extreme - lower extreme: $69 - 40 = 29$

Step6: Compute Dataset A IQR

IQR = Q3 - Q1: $67 - 46 = 21$

Step7: Calculate Dataset A mean

Mean = $\frac{40+42+46+48+51+55+58+66+67+68+69}{11} = \frac{610}{11} \approx 55.45$

Step8: Find Dataset A mode

No repeated values: No mode

Step9: Sort Dataset B

$1, 5, 8, 10, 11, 12, 14, 17, 19, 20, 22, 23$

Step10: Find Dataset B extremes

Lower extreme = smallest value: $1$
Upper extreme = largest value: $23$

Step11: Calculate Dataset B median

Average of 6th and 7th terms: $\frac{12+14}{2} = 13$

Step12: Find Dataset B quartiles

Lower quartile (Q1): median of first 6 terms: $\frac{8+10}{2} = 9$
Upper quartile (Q3): median of last 6 terms: $\frac{19+20}{2} = 19.5$

Step13: Compute Dataset B range

Range = upper extreme - lower extreme: $23 - 1 = 22$

Step14: Compute Dataset B IQR

IQR = Q3 - Q1: $19.5 - 9 = 10.5$

Step15: Calculate Dataset B mean

Mean = $\frac{1+5+8+10+11+12+14+17+19+20+22+23}{12} = \frac{162}{12} = 13.5$

Step16: Find Dataset B mode

No repeated values: No mode

Answer:

Dataset A Answers:

1. Lower Extreme: 40
2. Upper Extreme: 69
3. Median: 55
4. Lower Quartile: 46
5. Upper Quartile: 67
6. Range: 29
7. Interquartile Range: 21
8. Mean: $\frac{610}{11} \approx 55.45$
9. Mode: No mode

Dataset B Answers:

1. Lower Extreme: 1
2. Upper Extreme: 23
3. Median: 13
4. Lower Quartile: 9
5. Upper Quartile: 19.5
6. Range: 22
7. Interquartile Range: 10.5
8. Mean: 13.5
9. Mode: No mode