Question

practice: measures of central tendency
directions: find the mean, median, mode, and range of the following data sets.

1. 8, 3, 6, 9, 7, 9, 8

mean:
median:
mode:
range:

1. 6, 3, 8, 6, 6, 5, 8

mean:
median:
mode:
range:

1. 4, 3, 2, 9, 7, 7

mean:
median:
mode:
range:

1. 10, 6, 3, 10, 1, 5

mean:
median:
mode:
range:

1. 100%, 92%, 75%, 80%, 65%, 88%

mean:
median:
mode:
range:

1. 1, 0, 2, 3, 2, 0, 1, 4, 5, 1

mean:
median:
mode:
range:

Explanation:

---

Data Set 1: 8, 3, 6, 9, 7, 9, 8

Step1: Calculate the mean

Sum the values, divide by count:
$\text{Mean} = \frac{8+3+6+9+7+9+8}{7} = \frac{50}{7} \approx 7.14$

Step2: Calculate the median

Sort data: $3, 6, 7, 8, 8, 9, 9$. Middle value is 4th term:
$\text{Median} = 8$

Step3: Identify the mode

Most frequent values: 8 and 9 (each appears 2 times)
$\text{Mode} = 8, 9$

Step4: Calculate the range

Subtract min from max:
$\text{Range} = 9 - 3 = 6$

---

Data Set 2: 6, 3, 8, 6, 6, 5, 8

Step1: Calculate the mean

Sum the values, divide by count:
$\text{Mean} = \frac{6+3+8+6+6+5+8}{7} = \frac{42}{7} = 6$

Step2: Calculate the median

Sort data: $3, 5, 6, 6, 6, 8, 8$. Middle value is 4th term:
$\text{Median} = 6$

Step3: Identify the mode

Most frequent value: 6 (appears 3 times)
$\text{Mode} = 6$

Step4: Calculate the range

Subtract min from max:
$\text{Range} = 8 - 3 = 5$

---

Data Set 3: 4, 3, 2, 9, 7, 7

Step1: Calculate the mean

Sum the values, divide by count:
$\text{Mean} = \frac{4+3+2+9+7+7}{6} = \frac{32}{6} \approx 5.33$

Step2: Calculate the median

Sort data: $2, 3, 4, 7, 7, 9$. Average 3rd and 4th terms:
$\text{Median} = \frac{4+7}{2} = 5.5$

Step3: Identify the mode

Most frequent value: 7 (appears 2 times)
$\text{Mode} = 7$

Step4: Calculate the range

Subtract min from max:
$\text{Range} = 9 - 2 = 7$

---

Data Set 4: 10, 6, 3, 10, 1, 5

Step1: Calculate the mean

Sum the values, divide by count:
$\text{Mean} = \frac{10+6+3+10+1+5}{6} = \frac{35}{6} \approx 5.83$

Step2: Calculate the median

Sort data: $1, 3, 5, 6, 10, 10$. Average 3rd and 4th terms:
$\text{Median} = \frac{5+6}{2} = 5.5$

Step3: Identify the mode

Most frequent value: 10 (appears 2 times)
$\text{Mode} = 10$

Step4: Calculate the range

Subtract min from max:
$\text{Range} = 10 - 1 = 9$

---

Data Set 5: 100%, 92%, 75%, 80%, 65%, 88%

Step1: Calculate the mean

Sum the values, divide by count:
$\text{Mean} = \frac{100+92+75+80+65+88}{6}\% = \frac{500}{6}\% \approx 83.33\%$

Step2: Calculate the median

Sort data: $65\%, 75\%, 80\%, 88\%, 92\%, 100\%$. Average 3rd and 4th terms:
$\text{Median} = \frac{80+88}{2}\% = 84\%$

Step3: Identify the mode

All values appear once:
$\text{Mode} = \text{No mode}$

Step4: Calculate the range

Subtract min from max:
$\text{Range} = 100\% - 65\% = 35\%$

---

Data Set 6: 1, 0, 2, 3, 2, 0, 1, 4, 5, 1

Step1: Calculate the mean

Sum the values, divide by count:
$\text{Mean} = \frac{1+0+2+3+2+0+1+4+5+1}{10} = \frac{19}{10} = 1.9$

Step2: Calculate the median

Sort data: $0, 0, 1, 1, 1, 2, 2, 3, 4, 5$. Average 5th and 6th terms:
$\text{Median} = \frac{1+2}{2} = 1.5$

Step3: Identify the mode

Most frequent value: 1 (appears 3 times)
$\text{Mode} = 1$

Step4: Calculate the range

Subtract min from max:
$\text{Range} = 5 - 0 = 5$

Answer:

1. Mean: $\frac{50}{7} \approx 7.14$, Median: $8$, Mode: $8, 9$, Range: $6$
2. Mean: $6$, Median: $6$, Mode: $6$, Range: $5$
3. Mean: $\frac{32}{6} \approx 5.33$, Median: $5.5$, Mode: $7$, Range: $7$
4. Mean: $\frac{35}{6} \approx 5.83$, Median: $5.5$, Mode: $10$, Range: $9$
5. Mean: $\approx 83.33\%$, Median: $84\%$, Mode: No mode, Range: $35\%$
6. Mean: $1.9$, Median: $1.5$, Mode: $1$, Range: $5$