I need mean, median, and mode for the frequency table.

Mean: 16.67, Median: 16, Mode: 16

Step-by-step explanation:

Mean: add up all numbers and divide by how many there are.

But when you see the age 14, its frequency is 5; it's as if you wrote 14 down 5 times.  Frequency tables help describe long lists of data. So "adding up all numbers" would mean you could expand the list and add them all. HORRIBLE!

14+14+14+14+14+15+15+15+15+15+15+15+15+15+15+ ...  There is a better way:

Multiply each age by its frequency and add the products.

14(5)+15(9)+16(18)+17(11)+18(9)+19(5)+20(4) = 1017.  How many data values are there?  Add the frequencies

5+9+18+11+9+5+4 = 61

The mean is 1017 / 61 = 16.67 (rounded).

Median:  We need the number in the middle of the data list, but the numbers have been grouped by frequency.  There are 61 data values.  The one in the middle must be the 31st number (30 numbers less than the median, 30 numbers greater than the median).

Add up frequencies starting with the first one until you can tell where & what the 31st age is.

5

5+9 = 14

5 + 9 + 18 = 32  Aha!  The 31st age must be one of the 16s.

The median is 16.

Mode: is there an age that occurs more often than any of the others?  Yes, it is 16, which occurs 18 times.  No other age occurs that often.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

12

step-by-step explanation: