Harry Roberts, Washington, D.C., writes.

"My 9-month-old avocado is about 30 inches tall. It is growing in a large pot of soil indoors by a window. Most of the leaves brown at the tips and dry after attaining their growth size. Any tips on growing avocado inside would be appreciated; how often should it be watered? Does it need fertilizer?"

A. A plant cannot restore leaves that have gotten withered and dry, so it is best to cut them off; they do not contribute to the appearance or the growth of the plant.

Frequently more than one problem or deficiency is the cause of browning of leaf tips, among which are: Improper watering - avocados like lots of water; when you water, apply water until it runs out the drain hole of the pot; after half an hour, empty the saucer. Water again when the first inch of soil in the pot feels dry.

Excess fertilizer: Since you ask about fertilizer, this is apparently not your problem. During the winter months of shorter days, your plant will not need as much fertilizer or water as in the summer. Beginning in February or March, feed it once a month with a general houseplant fertilizer diluted to half the strength recommended by the manufacturer.

Exposure to cold drafts will brown leaf tips.

Low humidity: Increase humidity by setting the pot on a pebble tray; the tray should be deep enough to hold an inch of pebbles or marble chips and one-half inch of water. Evaporation of water from the surface of the pebbles will increase humidity around the plant.

Insect attact: Check your plant for pests. Wash the leaves with mild soapy water and rinse to remove insects.

Your avocado should flourish in a sunny window. If it is taller than you want it to be, you can cause it to branch by cutting it back. Make the cut at a point just above a good pair of leaves, at the height at which you would like for it to branch. In the axils where those leaves join the trunk are the buds from which new branches can be expected to develop.

Mrs. L. Leibowitz, Rockville, Md., writes: My Dieffenbachia produces new leaves which lean over and die before unfurling.

A. When leaves of Dieffenbachia droop and fall, examine the plant for mealy bugs. These sap-sucking pests appear as a white cottony mass at the point where a leaf joins the trunk of the plant. Use a cotton swab dipped in alcohol to remove the pests. Rinse with clear water.

When new growth seems to be hindered or existing leaves begin to curl, suspect aphids. Aphids are minute insects, brown, black or greenish, which suck plant juices. Frequent washing with mild soapy water is the way to remove them from the plant. Rinse with clear water.

Either of these treatments may need to be repeated until no further generations of insects appear.

A quick, accurate diagnosis is necessary in pinpointing houseplant problems. Researchers in the State College of Agriculture and Life Sciences at Cornell University point out that symptoms frequently mistaken for diseases are often the result of unfavorable conditions under which houseplants grow. For example, when philodendrons are grown under insufficient light, the lower leaves turn yellow, new leaves become undersized, and growing tips turn brown and die.

Statistics show that college registration in the field of horticultural studies has doubled, tripled and in many cases quadrupled over the last 10 years. Florist magazine conducted a survey of college professors, their students and the employers who have hired them to examine the reasons for the tremendous attraction horticulture holds for today's students, what they hope to accomplish, what they hope for the future and how the industry feels about this new group of horticulturists.

Of those interviewed, most agreed that the primary reason for the upsurge in horticultural interest is the result of the general greater awareness of our environment - both indoors and out.

Many students in college for another vocation switched to horticulture after dabbling in it as an elective. More women are becoming interested in this field, which was once considered predominantly a male field.

To best prepare them for their various horticultural vocations, collegiate studies are usually divided into at least two parts - textbook knowledge and practical experience. College professors feel that in addition to gaining confidence, the students also discover just how much they have yet to learn by working out in the field, and work experience makes them much more attractive employee prospects upon graduation.

Some of these students will become professional horticulturists whom you as an indoor gardener may have occasion to consult at plant stores and nurseries, in extension service offices, at botanic gardens and arboreta or in special horticulture classes.

If you have recently bought a dracaena, a philodendron, a Chinese evergreen, or some other favorite foliage plant, chances are that it came from Florida. According to the crop reporting service of the U.S. Department of Agriculture, most of the foliage plants grown in AMerica originate in Florida, and in wholesale sales Florida ranks way ahead of California and Texas, two other leaders in production of green plants.

During the busy months of February, March and April more than a million plants leave Florida daily, mostly by truck, some by air. The indoor foliage plantsmen grow more than 450 different species of plants. Commercial growers in the vicinity of Apopka, Fla., devote most of their energy to small plants, such as philodendron, dracaena and schefflera. South Florida nurseries grow mostly larger plants like palms, Ficus and cane varieties.

A housplant laboratory was established near Apopka in 1969. It is the only one in the world exclusively researching tropical foliage. Such work as soil composition, shade factors necessary to make plants thrive under home conditions, interactions between light intensities, developments in watering and fertilizers, and disease and pest control studies are a continuing program.

This research when applied to production of plants in specialized nurseries, makes it possible for the indoor gardener to obtain better plants in greater variety. The U.S. Department of Agriculture estimates that the average American household now has eight to 10 plants. Some of the most confirmed indoor gardeners probably exceed this average.