Given Frequency Distribution:

Income (in thousands) | No. of Persons
---------------------|--------------
Below 30 | 16
Below 40 | 36
Below 50 | 61
50-60 | 15
Below 70 | 87
Below 80 | 95
80 and above | 5

Arithmetic Mean:

The arithmetic mean of a frequency distribution is calculated by using the following formula:

`Mean = (sum of (frequency x midpoint))/n`

Where,
- n = sum of frequencies
- midpoint = (lower limit + upper limit)/2

Using this formula, we can calculate the mean income as:

`Mean = (16*15 + 36*35 + 61*45 + 15*55 + 87*65 + 95*75 + 5*85)/320`

`Mean = 54.25 thousand`

Therefore, the arithmetic mean income is 54.25 thousand.

Median:

The median of a frequency distribution is the value that lies in the middle when the data is arranged in ascending or descending order. To find the median income, we need to first calculate the cumulative frequency distribution.

Income (in thousands) | No. of Persons | Cumulative Frequency
---------------------|---------------|---------------------
Below 30 | 16 | 16
Below 40 | 36 | 52
Below 50 | 61 | 113
50-60 | 15 | 128
Below 70 | 87 | 215
Below 80 | 95 | 310
80 and above | 5 | 315

The median income is the value that lies in the middle, i.e., the 158th value. From the cumulative frequency distribution, we can see that this value lies in the "Below 70" income range. To find the exact median income, we use the following formula:

`Median = l + ((n/2 - F)/f) * w`

Where,
- l = lower limit of the median class
- n = sum of frequencies
- F = cumulative frequency up to the median class
- f = frequency of the median class
- w = width of the median class (upper limit - lower limit)

Using this formula, we get:

`Median = 50 + ((158 - 113)/87) * 20`

`Median = 63.22 thousand`

Therefore, the median income is 63.22 thousand.

Quartiles:

The quartiles divide the data into four equal parts. The first quartile (Q1) is the value that lies 25% of the way from the bottom, the second quartile (Q2) is the median, and the third quartile (Q3) is the value that lies 75% of the way from the bottom.

To find the quartiles, we can use the cumulative frequency distribution table.

- Q1: The first quartile is the value that lies 25% of the way from the bottom. This value lies in the "Below 40" income range. Using the formula for finding the median, we get:

`Q1 = 40 + ((80 - 16)/36) * 10`

`Q1 = 43.89 thousand`

- Q2: The second quartile