Question

Temperature are recorded every 1 hour for eleven hours from 6.00 am onwards in town.the average of first 6 reading is 30 and last six reading is 20 .overall temperature is 26 find the reading

Answer 1

The reading at 12 pm is 14°

Step-by-step explanation:

As per the question, Temperature are recorded every 1 hour for eleven hours from 6.00 am onwards in town. That means there are only 11 readings.

Starting from 6.00 am, the 6th reading is recorded in 12.00pm.

Let the 11 readings are denoted as r1, r2, r3, .... r11

The average of first 6 reading is 30

=> $30 = \frac{r1 + r2 + r3 + r4 + r5 + r6}{6}$

=> r1 + r2 + r3 + r4 + r5 + r6 = $30 \times 6$

=> r1 + r2 + r3 + r4 + r5 + r6 = 180  ----------------------- 1

The average of last six reading is 20

=> $20 = \frac{r6 + r7 + r8 + r9 + r10 + r11}{6}$

=> r6 + r7 + r8 + r9 + r10 + r11 = $20 \times 6$

=> r6 + r7 + r8 + r9 + r10 + r11 = 120   ----------------------- 2

The overall average of readings is 26

=> $26 = \frac{r1 + r2 + r3 + r4 + r5 + r6 + r7 + r8 + r9 + r10 + r11}{11}$

=> r1 + r2 + r3 + r4 + r5 + r6 + r7 + r8 + r9 + r10 + r11 = 286   -------------3

Now adding equation 1 and 2 we get,

=> r1 + r2 + r3 + r4 + r5 + r6 + r7 + r8 + r9 + r10 + r11 +r6 = 300

=> 286 + r6 = 300        ( from equation 3)

=> r6 = 14°

The reading at 12 pm is 14°

Answer 2

Answer:

14°C

Step-by-step explanation:

AVE [1 → 6] = 30°C

AVE [6 → 11] = 20°C

AVE [1 → 11] = 26°C

Total Value [1 → 6] = n * a : n = number of readings; a = average

Total Value [1 → 6] = (6) * (30) = 180

Total Value [6 → 11] = (6) * (20) = 120

Total Value [1 → 11] = (11) * (26) = 286

So we can see that if we add the value from [1 → 6] and [6 → 11], 6 will be counted twice.

[1 → 6] + [6 → 11] = 180 + 120 = 300

Subtracting this from the Total Value [1 → 11] will leave only the twice counted Value [6]:

300 - 286 = 14°C