Calculate the mean of the following sets of data.
| Value | Frequency |
|---|---|
| 1 | 3 |
| 4 | 5 |
| 7 | 8 |
The frequency table represents values in a set and the number of times that each value is repeated in the set. The mean of a set of data is given by the formula:
\overline{x}=\dfrac{\sum x_i.n_i}{N}
\overline{x} is the mean of the set, x_i is the i^{\rm th} element in the set , n_i is the number of times that value is found in the set and N is the number of elements in the set.
Here:
- Value 1 is repeated 3 times.
- Value 4 is repeated 5 times.
- Value 7 is repeated 8 times.
Hence:
\sum x_i.n_i=1\times3+4\times5 + 7\times8 = 79\\
And:
N=3+5+8=16
Therefore the mean of this set of data is:
\overline{x}=\dfrac{79}{16}
The mean of this set of data is \dfrac{79}{16}.
| Value | Frequency |
|---|---|
| 2 | 4 |
| 4 | 10 |
| 5 | 2 |
| 19 | 1 |
The frequency table represents values in a set and the number of times that each value is repeated in the set. The mean of a set of data is given by the formula:
\overline{x}=\dfrac{\sum x_i.n_i}{N}
\overline{x} is the mean of the set, x_i is the i^{\rm th} element in the set , n_i is the number of times that value is found in the set and N is the number of elements in the set.
Here:
- Value 2 is repeated 4 times.
- Value 4 is repeated 10 times.
- Value 5 is repeated 2 times.
- Value 19 is repeated 1 time.
Hence:
\sum x_i.n_i=\left(2\times4\right)+\left(4\times10\right) + \left(5\times2\right)+\left(19\times1\right) = 77
And:
N=4+10+2+1=17
Therefore the mean of this set of data is:
\overline{x}=\dfrac{77}{17}
The mean of this set of data is \dfrac{77}{17}.
| Value | Frequency |
|---|---|
| 4 | 1 |
| 7 | 1 |
| 16 | 1 |
| 17 | 2 |
| 20 | 2 |
The frequency table represents values in a set and the number of times that each value is repeated in the set. The mean of a set of data is given by the formula:
\overline{x}=\dfrac{\sum x_i.n_i}{N}
\overline{x} is the mean of the set, x_i is the i^{\rm th} element in the set , n_i is the number of times that value is found in the set and N is the number of elements in the set.
Here:
- Value 4 is repeated 1 time.
- Value 7 is repeated 1 time.
- Value 16 is repeated 1 time.
- Value 17 is repeated 2 times.
- Value 20 is repeated 2 time
Hence:
\sum x_i.n_i=\left(4 \times1\right) + \left(7 \times1\right) + \left(16 \times1\right) + \left(17 \times2\right) + \left(20 \times2\right)=101
And:
N=1+1+1+2+2=7
Therefore the mean of this set of data is:
\overline{x}=\dfrac{101}{7}
The mean of this set of data is \dfrac{101}{7}.
| Value | Frequency |
|---|---|
| 1 | 2 |
| 2 | 6 |
| 5 | 2 |
| 6 | 2 |
The frequency table represents values in a set and the number of times that each value is repeated in the set. The mean of a set of data is given by the formula:
\overline{x}=\dfrac{\sum x_i.n_i}{N}
\overline{x} is the mean of the set, x_i is the i^{\rm th} element in the set , n_i is the number of times that value is found in the set and N is the number of elements in the set.
Here:
- Value 1 is repeated 2 times.
- Value 2 is repeated 6 times.
- Value 5 is repeated 2 times.
- Value 6 is repeated 2 time.
Hence:
\sum x_i.n_i=\left(1\times2\right)+\left(2\times6\right) + \left(5\times2\right)+\left(6\times2\right) = 36
And:
N=2+6+2+2=12
Therefore the mean of this set of data is:
\overline{x}=\dfrac{36}{12}=3
The mean of this set of data is \dfrac{36}{12}=3.
\{2, 3, 5, 7, 9, 12, 13, 15\}
The frequency table represents values in a set and the number of times that each value is repeated in the set. The mean of a set of data is given by the formula:
\overline{x}=\dfrac{\sum x_i.n_i}{N}
\overline{x} is the mean of the set, x_i is the i^{\rm th} element in the set , n_i is the number of times that value is found in the set and N is the number of elements in the set.
Here:
\overline{x} = \dfrac{2+3+5+7+9+12+13+15}{8} = \dfrac{66}{8} = \dfrac{33}{4}
The mean of this set of data is \dfrac{33}{4}.
\{1, 1, 2, 3, 6, 7, 7, 7, 8, 10\}
The frequency table represents values in a set and the number of times that each value is repeated in the set. The mean of a set of data is given by the formula:
\overline{x}=\dfrac{\sum x_i.n_i}{N}
\overline{x} is the mean of the set, x_i is the i^{\rm th} element in the set , n_i is the number of times that value is found in the set and N is the number of elements in the set.
Here:
\overline{x} = \dfrac{1+1+2+3+6+7+7+7+8+10}{10} = \dfrac{52}{10} = 5.2
The mean of this set of data is 5.2.
| Value | Frequency |
|---|---|
| 5 | 15 |
| 6 | 2 |
| 7 | 1 |
| 10 | 3 |
| 14 | 4 |
The frequency table represents values in a set and the number of times that each value is repeated in the set. The mean of a set of data is given by the formula:
\overline{x}=\dfrac{\sum x_i.n_i}{N}
\overline{x} is the mean of the set, x_i is the i^{\rm th} element in the set , n_i is the number of times that value is found in the set and N is the number of elements in the set.
Here:
- Value 5 is repeated 15 time.
- Value 6 is repeated 2 time.
- Value 7 is repeated 1 time.
- Value 10 is repeated 3 times.
- Value 14 is repeated 4 time
Hence:
\sum x_i.n_i=\left(5 \times15\right)+\left(6 \times2\right)+\left(7 \times1\right)+\left(10 \times3\right)+\left(14 \times4\right)=180
And:
N=15+2+ 1+ 3+ 4=25
Therefore the mean of this set of data is:
\overline{x}=\dfrac{180}{25} = 7.2
The mean of this set of data is 7.2