Advertisements
Advertisements
प्रश्न
The arithmetic mean of 1, 2, 3, ... , n is
विकल्प
\[\frac{n + 1}{2}\]
\[\frac{n - 1}{2}\]
\[\frac{n}{2}\]
\[\frac{n}{2} + 1\]
उत्तर
Arithmetic mean of 1, 2, 3, ... , n
\[= \frac{1 + 2 + 3 + . . . + n}{n}\]
\[ = \frac{\frac{n\left( n + 1 \right)}{2}}{n}\]
\[ = \frac{n + 1}{2}\]
Hence, the correct option is (a).
APPEARS IN
संबंधित प्रश्न
Find the mean of each of the following frequency distributions
| Class interval | 0 - 8 | 8 - 16 | 16 - 24 | 24 - 32 | 32 - 40 |
| Frequency | 5 | 6 | 4 | 3 | 2 |
During a medical check-up, the number of heartbeats per minute of 30 patients were recorded and summarized as follows:
| Number of heartbeats per minute |
65 – 68 | 68 – 71 | 71 – 74 | 74 – 77 | 77 – 80 | 80 – 83 | 83 - 86 |
| Number of patients |
2 | 4 | 3 | 8 | 7 | 4 | 2 |
Find the mean heartbeats per minute for these patients, choosing a suitable method.
The weights of tea in 70 packets are shown in the following table:
| Weight | 200 – 201 |
201 – 202 |
202 – 203 |
203 – 204 |
204 – 205 |
205 – 206 |
| Number of packets | 13 | 27 | 18 | 10 | 1 | 1 |
Find the mean weight of packets using step deviation method.
A school has 4 sections of Chemistry in class X having 40, 35, 45 and 42 students. The mean marks obtained in Chemistry test are 50, 60, 55 and 45 respectively for the 4 sections. Determine the overall average of marks per student.
Mean of n numbers x1, x2, … xn is m. If xn is replaced by x, then new mean is ______.
The mean of the following distribution is
| xi | 10 | 13 | 16 | 19 |
| fi | 2 | 5 | 7 | 6 |
There is a grouped data distribution for which mean is to be found by step deviation method.
| Class interval | Number of Frequency (fi) | Class mark (xi) | di = xi - a | `u_i=d_i/h` |
| 0 - 100 | 40 | 50 | -200 | D |
| 100 - 200 | 39 | 150 | B | E |
| 200 - 300 | 34 | 250 | 0 | 0 |
| 300 - 400 | 30 | 350 | 100 | 1 |
| 400 - 500 | 45 | 450 | C | F |
| Total | `A=sumf_i=....` |
Find the value of A, B, C, D, E and F respectively.
While computing mean of grouped data, we assume that the frequencies are ______.
The following table gives the duration of movies in minutes:
| Duration | 100 – 110 | 110 – 120 | 120 – 130 | 130 – 140 | 140 – 150 | 150 – 160 |
| No. of movies | 5 | 10 | 17 | 8 | 6 | 4 |
Using step-deviation method, find the mean duration of the movies.
Using step-deviation method, find mean for the following frequency distribution:
| Class | 0 – 15 | 15 – 30 | 30 – 45 | 45 – 60 | 60 – 75 | 75 – 90 |
| Frequency | 3 | 4 | 7 | 6 | 8 | 2 |
